We study the following model for a system the state of which is continuously observed. The set of possible states is a finite set {0, . . . , L}, where larger values represent increased states of deterioration from the “new condition” represented by state 0, to the “totally inoperative condition” of state L. Whenever the system changes state a decision has to be made as to whether it is renovat...

We review how tools from multiplicative ergodic theory and the theory of positive operators are used in the analysis of exponential stability of the optimal nonlinear filter. Particularly, in the case of finite state, we relate the filter sensitivity to perturbations in its initial data to the Lyapunov spectral gap associated with the filtering equation, and, in a general setting, use Hilbert’s...

Dynamical nonlinear systems provide a new approach to the old problem of increasing the efficiency of thermoelectric machines. In this review, we discuss stylized models of classical dynamics, including non-interacting complex molecules in an ergodic billiard, a disordered hard-point gas and an abstract thermoelectric machine. The main focus will be on the physical mechanisms, unveiled by these...

We consider a single-asset investment fund that in the absence of transactions costs would hold a constant amount of wealth in the risky asset. In the presence of market frictions wealth is allowed to fluctuate within a control band: Its upper (lower) boundary is chosen so that gains (losses) from adjustments to the target minus (plus) fixed plus proportional transaction costs maximize (minimiz...

We investigate the stability problem for a nonlinear autoregressive model with Markov switching. First we give conditions for the existence and the uniqueness of a stationary ergodic solution. The existence of moments of such a solution is then examined and we establish a strong law of large numbers for a wide class of unbounded functions, as well as a central limit theorem under an irreducibil...